src/jpeg/jidctfst.c

   1 /*
   2  * jidctfst.c
   3  *
   4  * Copyright (C) 1994-1998, Thomas G. Lane.
   5  * This file is part of the Independent JPEG Group's software.
   6  * For conditions of distribution and use, see the accompanying README file.
   7  *
   8  * This file contains a fast, not so accurate integer implementation of the
   9  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
  10  * must also perform dequantization of the input coefficients.
  11  *
  12  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
  13  * on each row (or vice versa, but it's more convenient to emit a row at
  14  * a time).  Direct algorithms are also available, but they are much more
  15  * complex and seem not to be any faster when reduced to code.
  16  *
  17  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
  18  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
  19  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
  20  * JPEG textbook (see REFERENCES section in file README).  The following code
  21  * is based directly on figure 4-8 in P&M.
  22  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
  23  * possible to arrange the computation so that many of the multiplies are
  24  * simple scalings of the final outputs.  These multiplies can then be
  25  * folded into the multiplications or divisions by the JPEG quantization
  26  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
  27  * to be done in the DCT itself.
  28  * The primary disadvantage of this method is that with fixed-point math,
  29  * accuracy is lost due to imprecise representation of the scaled
  30  * quantization values.  The smaller the quantization table entry, the less
  31  * precise the scaled value, so this implementation does worse with high-
  32  * quality-setting files than with low-quality ones.
  33  */
  34
  35 #define JPEG_INTERNALS
  36 #include "jinclude.h"
  37 #include "jpeglib.h"
  38 #include "jdct.h"               /* Private declarations for DCT subsystem */
  39
  40 #ifdef DCT_IFAST_SUPPORTED
  41
  42
  43 /*
  44  * This module is specialized to the case DCTSIZE = 8.
  45  */
  46
  47 #if DCTSIZE != 8
  48   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  49 #endif
  50
  51
  52 /* Scaling decisions are generally the same as in the LL&M algorithm;
  53  * see jidctint.c for more details.  However, we choose to descale
  54  * (right shift) multiplication products as soon as they are formed,
  55  * rather than carrying additional fractional bits into subsequent additions.
  56  * This compromises accuracy slightly, but it lets us save a few shifts.
  57  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
  58  * everywhere except in the multiplications proper; this saves a good deal
  59  * of work on 16-bit-int machines.
  60  *
  61  * The dequantized coefficients are not integers because the AA&N scaling
  62  * factors have been incorporated.  We represent them scaled up by PASS1_BITS,
  63  * so that the first and second IDCT rounds have the same input scaling.
  64  * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
  65  * avoid a descaling shift; this compromises accuracy rather drastically
  66  * for small quantization table entries, but it saves a lot of shifts.
  67  * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
  68  * so we use a much larger scaling factor to preserve accuracy.
  69  *
  70  * A final compromise is to represent the multiplicative constants to only
  71  * 8 fractional bits, rather than 13.  This saves some shifting work on some
  72  * machines, and may also reduce the cost of multiplication (since there
  73  * are fewer one-bits in the constants).
  74  */
  75
  76 #if BITS_IN_JSAMPLE == 8
  77 #define CONST_BITS  8
  78 #define PASS1_BITS  2
  79 #else
  80 #define CONST_BITS  8
  81 #define PASS1_BITS  1           /* lose a little precision to avoid overflow */
  82 #endif
  83
  84 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  85  * causing a lot of useless floating-point operations at run time.
  86  * To get around this we use the following pre-calculated constants.
  87  * If you change CONST_BITS you may want to add appropriate values.
  88  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  89  */
  90
  91 #if CONST_BITS == 8
  92 #define FIX_1_082392200  ((JPEG_INT32)  277)            /* FIX(1.082392200) */
  93 #define FIX_1_414213562  ((JPEG_INT32)  362)            /* FIX(1.414213562) */
  94 #define FIX_1_847759065  ((JPEG_INT32)  473)            /* FIX(1.847759065) */
  95 #define FIX_2_613125930  ((JPEG_INT32)  669)            /* FIX(2.613125930) */
  96 #else
  97 #define FIX_1_082392200  FIX(1.082392200)
  98 #define FIX_1_414213562  FIX(1.414213562)
  99 #define FIX_1_847759065  FIX(1.847759065)
 100 #define FIX_2_613125930  FIX(2.613125930)
 101 #endif
 102
 103
 104 /* We can gain a little more speed, with a further compromise in accuracy,
 105  * by omitting the addition in a descaling shift.  This yields an incorrectly
 106  * rounded result half the time...
 107  */
 108
 109 #ifndef USE_ACCURATE_ROUNDING
 110 #undef DESCALE
 111 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
 112 #endif
 113
 114
 115 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
 116  * descale to yield a DCTELEM result.
 117  */
 118
 119 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
 120
 121
 122 /* Dequantize a coefficient by multiplying it by the multiplier-table
 123  * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16
 124  * multiplication will do.  For 12-bit data, the multiplier table is
 125  * declared INT32, so a 32-bit multiply will be used.
 126  */
 127
 128 #if BITS_IN_JSAMPLE == 8
 129 #define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval))
 130 #else
 131 #define DEQUANTIZE(coef,quantval)  \
 132         DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
 133 #endif
 134
 135
 136 /* Like DESCALE, but applies to a DCTELEM and produces an int.
 137  * We assume that int right shift is unsigned if INT32 right shift is.
 138  */
 139
 140 #ifdef RIGHT_SHIFT_IS_UNSIGNED
 141 #define ISHIFT_TEMPS    DCTELEM ishift_temp;
 142 #if BITS_IN_JSAMPLE == 8
 143 #define DCTELEMBITS  16         /* DCTELEM may be 16 or 32 bits */
 144 #else
 145 #define DCTELEMBITS  32         /* DCTELEM must be 32 bits */
 146 #endif
 147 #define IRIGHT_SHIFT(x,shft)  \
 148     ((ishift_temp = (x)) < 0 ? \
 149      (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
 150      (ishift_temp >> (shft)))
 151 #else
 152 #define ISHIFT_TEMPS
 153 #define IRIGHT_SHIFT(x,shft)    ((x) >> (shft))
 154 #endif
 155
 156 #ifdef USE_ACCURATE_ROUNDING
 157 #define IDESCALE(x,n)  ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
 158 #else
 159 #define IDESCALE(x,n)  ((int) IRIGHT_SHIFT(x, n))
 160 #endif
 161
 162
 163 /*
 164  * Perform dequantization and inverse DCT on one block of coefficients.
 165  */
 166
 167 GLOBAL(void)
 168 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
 169                  JCOEFPTR coef_block,
 170                  JSAMPARRAY output_buf, JDIMENSION output_col)
 171 {
 172   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 173   DCTELEM tmp10, tmp11, tmp12, tmp13;
 174   DCTELEM z5, z10, z11, z12, z13;
 175   JCOEFPTR inptr;
 176   IFAST_MULT_TYPE * quantptr;
 177   int * wsptr;
 178   JSAMPROW outptr;
 179   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
 180   int ctr;
 181   int workspace[DCTSIZE2];      /* buffers data between passes */
 182   SHIFT_TEMPS                   /* for DESCALE */
 183   ISHIFT_TEMPS                  /* for IDESCALE */
 184
 185   /* Pass 1: process columns from input, store into work array. */
 186
 187   inptr = coef_block;
 188   quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
 189   wsptr = workspace;
 190   for (ctr = DCTSIZE; ctr > 0; ctr--) {
 191     /* Due to quantization, we will usually find that many of the input
 192      * coefficients are zero, especially the AC terms.  We can exploit this
 193      * by short-circuiting the IDCT calculation for any column in which all
 194      * the AC terms are zero.  In that case each output is equal to the
 195      * DC coefficient (with scale factor as needed).
 196      * With typical images and quantization tables, half or more of the
 197      * column DCT calculations can be simplified this way.
 198      */
 199
 200     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
 201         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
 202         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
 203         inptr[DCTSIZE*7] == 0) {
 204       /* AC terms all zero */
 205       int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 206
 207       wsptr[DCTSIZE*0] = dcval;
 208       wsptr[DCTSIZE*1] = dcval;
 209       wsptr[DCTSIZE*2] = dcval;
 210       wsptr[DCTSIZE*3] = dcval;
 211       wsptr[DCTSIZE*4] = dcval;
 212       wsptr[DCTSIZE*5] = dcval;
 213       wsptr[DCTSIZE*6] = dcval;
 214       wsptr[DCTSIZE*7] = dcval;
 215
 216       inptr++;                  /* advance pointers to next column */
 217       quantptr++;
 218       wsptr++;
 219       continue;
 220     }
 221
 222     /* Even part */
 223
 224     tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 225     tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
 226     tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
 227     tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
 228
 229     tmp10 = tmp0 + tmp2;        /* phase 3 */
 230     tmp11 = tmp0 - tmp2;
 231
 232     tmp13 = tmp1 + tmp3;        /* phases 5-3 */
 233     tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
 234
 235     tmp0 = tmp10 + tmp13;       /* phase 2 */
 236     tmp3 = tmp10 - tmp13;
 237     tmp1 = tmp11 + tmp12;
 238     tmp2 = tmp11 - tmp12;
 239
 240     /* Odd part */
 241
 242     tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
 243     tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
 244     tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
 245     tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
 246
 247     z13 = tmp6 + tmp5;          /* phase 6 */
 248     z10 = tmp6 - tmp5;
 249     z11 = tmp4 + tmp7;
 250     z12 = tmp4 - tmp7;
 251
 252     tmp7 = z11 + z13;           /* phase 5 */
 253     tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
 254
 255     z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
 256     tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
 257     tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
 258
 259     tmp6 = tmp12 - tmp7;        /* phase 2 */
 260     tmp5 = tmp11 - tmp6;
 261     tmp4 = tmp10 + tmp5;
 262
 263     wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
 264     wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
 265     wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
 266     wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
 267     wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
 268     wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
 269     wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
 270     wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
 271
 272     inptr++;                    /* advance pointers to next column */
 273     quantptr++;
 274     wsptr++;
 275   }
 276
 277   /* Pass 2: process rows from work array, store into output array. */
 278   /* Note that we must descale the results by a factor of 8 == 2**3, */
 279   /* and also undo the PASS1_BITS scaling. */
 280
 281   wsptr = workspace;
 282   for (ctr = 0; ctr < DCTSIZE; ctr++) {
 283     outptr = output_buf[ctr] + output_col;
 284     /* Rows of zeroes can be exploited in the same way as we did with columns.
 285      * However, the column calculation has created many nonzero AC terms, so
 286      * the simplification applies less often (typically 5% to 10% of the time).
 287      * On machines with very fast multiplication, it's possible that the
 288      * test takes more time than it's worth.  In that case this section
 289      * may be commented out.
 290      */
 291
 292 #ifndef NO_ZERO_ROW_TEST
 293     if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
 294         wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
 295       /* AC terms all zero */
 296       JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
 297                                   & RANGE_MASK];
 298
 299       outptr[0] = dcval;
 300       outptr[1] = dcval;
 301       outptr[2] = dcval;
 302       outptr[3] = dcval;
 303       outptr[4] = dcval;
 304       outptr[5] = dcval;
 305       outptr[6] = dcval;
 306       outptr[7] = dcval;
 307
 308       wsptr += DCTSIZE;         /* advance pointer to next row */
 309       continue;
 310     }
 311 #endif
 312
 313     /* Even part */
 314
 315     tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
 316     tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
 317
 318     tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
 319     tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
 320             - tmp13;
 321
 322     tmp0 = tmp10 + tmp13;
 323     tmp3 = tmp10 - tmp13;
 324     tmp1 = tmp11 + tmp12;
 325     tmp2 = tmp11 - tmp12;
 326
 327     /* Odd part */
 328
 329     z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
 330     z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
 331     z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
 332     z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
 333
 334     tmp7 = z11 + z13;           /* phase 5 */
 335     tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
 336
 337     z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
 338     tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
 339     tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
 340
 341     tmp6 = tmp12 - tmp7;        /* phase 2 */
 342     tmp5 = tmp11 - tmp6;
 343     tmp4 = tmp10 + tmp5;
 344
 345     /* Final output stage: scale down by a factor of 8 and range-limit */
 346
 347     outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
 348                             & RANGE_MASK];
 349     outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
 350                             & RANGE_MASK];
 351     outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
 352                             & RANGE_MASK];
 353     outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
 354                             & RANGE_MASK];
 355     outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
 356                             & RANGE_MASK];
 357     outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
 358                             & RANGE_MASK];
 359     outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
 360                             & RANGE_MASK];
 361     outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
 362                             & RANGE_MASK];
 363
 364     wsptr += DCTSIZE;           /* advance pointer to next row */
 365   }
 366 }
 367
 368 #endif /* DCT_IFAST_SUPPORTED */